Problem: Vanessa is 4 years younger than Kevin. For the last two years, Kevin and Vanessa have been going to the same school. Fifteen years ago, Kevin was 3 times older than Vanessa. How old is Kevin now?
Answer: We can use the given information to write down two equations that describe the ages of Kevin and Vanessa. Let Kevin's current age be $k$ and Vanessa's current age be $v$ The information in the first sentence can be expressed in the following equation: $k = v + 4$ Fifteen years ago, Kevin was $k - 15$ years old, and Vanessa was $v - 15$ years old. The information in the second sentence can be expressed in the following equation: $k - 15 = 3(v - 15)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $k$ , it might be easiest to solve our first equation for $v$ and substitute it into our second equation. Solving our first equation for $v$ , we get: $v = k - 4$ . Substituting this into our second equation, we get the equation: $k - 15 = 3($ $(k - 4)$ $ -$ $ 15)$ which combines the information about $k$ from both of our original equations. Simplifying the right side of this equation, we get: $k - 15 = 3k - 57$ Solving for $k$ , we get: $2 k = 42$ $k = 21$.